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Machine learning techniques have led to broad adoption of a statistical model of computing. The statistical distributions natively available on quantum processors are a superset of those available classically. Harnessing this attribute has the potential to accelerate or otherwise improve machine learning relative to purely classical performance. A key challenge toward that goal is learning to hybridize classical computing resources and traditional learning techniques with the emerging capabilities of general purpose quantum processors. Here, we demonstrate such hybridization by training a 19-qubit gate model processor to solve a clustering problem, a foundational challenge in unsupervised learning. We use the quantum approximate optimization algorithm in conjunction with a gradient-free Bayesian optimization to train the quantum machine. This quantum/classical hybrid algorithm shows robustness to realistic noise, and we find evidence that classical optimization can be used to train around both coherent and incoherent imperfections., Comment: 7 pages + appendix, many figures

We describe and implement a family of entangling gates activated by radio-frequency flux modulation applied to a tunable transmon that is statically coupled to a neighboring transmon. The effect of this modulation is the resonant exchange of photons directly between levels of the two-transmon system, obviating the need for mediating qubits or resonator modes and allowing for the full utilization of all qubits in a scalable architecture. The resonance condition is selective in both the frequency and amplitude of modulation and thus alleviates frequency crowding. We demonstrate the use of three such resonances to produce entangling gates that enable universal quantum computation: one iSWAP gate and two distinct controlled Z gates. We report interleaved randomized benchmarking results indicating gate error rates of 6% for the iSWAP (duration 135ns) and 9% for the controlled Z gates (durations 175 ns and 270 ns), limited largely by qubit coherence., Comment: As submitted. 7 pages, 6 figures

We show that parametric coupling techniques can be used to generate selective entangling interactions for multi-qubit processors. By inducing coherent population exchange between adjacent qubits under frequency modulation, we implement a universal gateset for a linear array of four superconducting qubits. An average process fidelity of $\mathcal{F}=93\%$ is estimated for three two-qubit gates via quantum process tomography. We establish the suitability of these techniques for computation by preparing a four-qubit maximally entangled state and comparing the estimated state fidelity against the expected performance of the individual entangling gates. In addition, we prepare an eight-qubit register in all possible bitstring permutations and monitor the fidelity of a two-qubit gate across one pair of these qubits. Across all such permutations, an average fidelity of $\mathcal{F}=91.6\pm2.6\%$ is observed. These results thus offer a path to a scalable architecture with high selectivity and low crosstalk.

We evaluate the topological character of TaAs through a detailed study of the angular, magnetic-field and temperature dependence of its magnetoresistivity and Hall-effect(s), and of its bulk electronic structure through quantum oscillatory phenomena. At low temperatures, and for fields perpendicular to the electrical current, we extract an extremely large Hall angle $\Theta_H$ at higher fields, that is $\Theta_H \sim 82.5^{\circ}$, implying a very pronounced Hall signal superimposed into its magnetoresistivity. For magnetic fields and electrical currents perpendicular to the \emph{c}-axis we observe a very pronounced planar Hall-effect, when the magnetic field is rotated within the basal plane. This effect is observed even at higher temperatures, i.e. as high as $T = 100$ K, and predicted recently to result from the chiral anomaly among Weyl points. Superimposed onto this planar Hall, which is an even function of the field, we observe an anomalous planar Hall-signal akin to the one reported for that is an odd function of the field. Below 100 K, negative longitudinal magnetoresistivity (LMR), initially ascribed to the chiral anomaly and subsequently to current inhomogeneities, is observed in samples having different geometries and contact configurations, once the large Hall signal is subtracted. Our measurements reveal a phase transition upon approaching the quantum limit that leads to the reconstruction of the FS and to the concomitant suppression of the negative LMR indicating that it is intrinsically associated with the Weyl dispersion at the Fermi level. For fields along the \emph{a}-axis it also leads to a pronounced hysteresis pointing to a field-induced electronic phase-transition. This collection of unconventional tranport observations points to the prominent role played by the axial anomaly among Weyl nodes., Comment: 13 pages, 8 figures, Supplemental File not included

We report the evolution of the surface electronic structure and surface material properties of a topological crystalline insulator (TCI) Pb1-xSnxSe as a function of various material parameters including composition x, temperature T and crystal structure. Our spectroscopic data demonstrate the electronic groundstate condition for the saddle point singularity, the tunability of surface chemical potential, and the surface states' response to circularly polarized light. Our results show that each material parameter can tune the system between trivial and topological phase in a distinct way unlike as seen in Bi2Se3 and related compounds, leading to a rich and unique topological phase diagram. Our systematic studies of the TCI Pb1-xSnxSe are valuable materials guide to realize new topological phenomena., Comment: 10 pages, 7 figures. Expanded version of arXiv:1403.1560

A topological Dirac semimetal is a novel state of quantum matter which has recently attracted much attention as an apparent 3D version of graphene. In this paper, we report critically important results on the electronic structure of the 3D Dirac semimetal Na3Bi at a surface that reveals its nontrivial groundstate. Our studies, for the first time, reveal that the two 3D Dirac cones go through a topological change in the constant energy contour as a function of the binding energy, featuring a Lifshitz point, which is missing in a strict 3D analog of graphene (in other words Na3Bi is not a true 3D analog of graphene). Our results identify the first example of a band saddle point singularity in 3D Dirac materials. This is in contrast to its 2D analogs such as graphene and the helical Dirac surface states of a topological insulator. The observation of multiple Dirac nodes in Na3Bi connecting via a Lifshitz point along its crystalline rotational axis away from the Kramers point serves as a decisive signature for the symmetry-protected nature of the Dirac semimetal's topological groundstate., Comment: 5 pages, 4 Figures, Related papers on topological Fermi arcs and Weyl Semimetals (WSMs) are at http://physics.princeton.edu/zahidhasangroup/index.html

A topological crystalline insulator (TCI) is a new phase of topological matter, which is predicted to exhibit distinct topological quantum phenomena, since space group symmetries replace the role of time-reversal symmetry in the much-studied Z$_2$ topological insulators. Utilizing high-resolution angle-resolved photoemission spectroscopy (ARPES), we reveal the momentum space nature of interconnectivity of the Fermi surface pockets leading to a saddle point singularity within the topological surface state alone in the TCI Pb$_{0.7}$Sn$_{0.3}$Se. Moreover, we show that the measured momentum-integrated density of states exhibits pronounced peaks at the saddle point energies, demonstrating the van Hove singularities (VHSs) in the topological surface states, whose surface chemical potential, as we show, can be tuned via surface chemical gating, providing access to the topological correlated physics on the surface. Our experimental data reveal a delicate relationship among lattice constant, band gap and spin-orbit coupling strength associated with the topological phase transition in Pb$_{1-x}$Sn$_{x}$Se. Furthermore, we explore the robustness of the TCI phase with VHS in Pb$_{1-x}$Sn$_{x}$Se, which shows a variety of distinct topological phase transitions driven by either thermal instability or broken crystalline symmetry, and thus revealing a rich topological phase diagram connectivity in Pb$_{1-x}$Sn$_{x}$Se for the first time., Comment: 18 pages, 4 figres

Symmetry or topology protected Dirac fermion states in two and three dimensions constitute novel quantum systems that exhibit exotic physical phenomena. However, none of the studied spin-orbit materials are suitable for realizing bulk multiplet Dirac states for the exploration of interacting Dirac physics. Here we present experimental evidence, for the first time, that the compound Na3Bi hosts a bulk spin-orbit Dirac multiplet and their interaction or overlap leads to a Lifshitz transition in momentum space - a condition for realizing interactions involving Dirac states. By carefully preparing the samples at a non-natural-cleavage (100) crystalline surface, we uncover many novel electronic and spin properties in Na3Bi by utilizing high resolution angle- and spin-resolved photoemission spectroscopy measurements. We observe two bulk 3D Dirac nodes that locate on the opposite sides of the bulk zone center point $\Gamma$, which exhibit a Fermi surface Lifshitz transition and a saddle point singularity. Furthermore, our data shows evidence for the possible existence of theoretically predicted weak 2D nontrivial spin-orbit surface state with helical spin polarization that are nestled between the two bulk Dirac cones, consistent with the theoretically calculated (100) surface-arc-modes. Our main experimental observation of a rich multiplet of Dirac structure and the Lifshitz transition opens the door for inducing electronic instabilities and correlated physical phenomena in Na3Bi, and paves the way for the engineering of novel topological states using Na3Bi predicted in recent theory., Comment: 23 pages, 5 Figures

Possible topological nature of Kondo and mixed valence insulators has been a recent topic of interest in condensed matter physics. Attention has focused on SmB6, which has long been known to exhibit low temperature transport anomaly, whose origin is of independent interest. We argue that it is possible to resolve the topological nature of surface states by uniquely accessing the surface electronic structure of the low temperature anomalous transport regime through combining state-of-the-art laser- and synchrotron-based angle-resolved photoemission spectroscopy (ARPES) with or without spin resolution. A combination of low temperature and ultra-high resolution (laser) which is lacking in previous ARPES studies of this compound is the key to resolve the possible existence of topological surface state in SmB6. Here we outline an experimental algorithm to systematically explore the topological versus trivial or mixed (topological and trivial surface state admixture as in the first 3D TI Bi$_{1-x}$Sb$_x$) nature of the surface states in Kondo and mixed valence insulators. We conclude based on this methodology that the observed topology of the surface Fermi surface in our low temperature data considered within the level of current resolution is consistent with the theoretically predicted topological picture, suggesting a topological origin of the dominant in-gap ARPES signal in SmB6.}, Comment: 15 pages, 6 Figures, Submitted June'13; Published as SI in Nature Commun. 4, 2991 (2013)

Topological insulators are characterized by Dirac cone surface states with electron spins aligned in the surface plane and perpendicular to their momenta. Recent theoretical and experimental work implied that this specific spin texture should enable control of photoelectron spins by circularly polarized light. However, these reports questioned the so far accepted interpretation of spin-resolved photoelectron spectroscopy. We solve this puzzle and show that vacuum ultraviolet photons (50-70 eV) with linear or circular polarization probe indeed the initial state spin texture of Bi$_2$Se$_3$ while circularly polarized 6 eV low energy photons flip the electron spins out of plane and reverse their spin polarization. Our photoemission calculations, considering the interplay between the varying probing depth, dipole selection rules and spin-dependent scattering effects involving initial and final states explain these findings, and reveal proper conditions for light-induced spin manipulation. This paves the way for future applications of topological insulators in opto-spintronic devices., Comment: Submitted for publication (2013)

Experimental identification of three-dimensional (3D) Dirac semimetals in solid state systems is critical for realizing exotic topological phenomena and quantum transport such as the Weyl phases, high temperature linear quantum magnetoresistance and topological magnetic phases. Using high resolution angle-resolved photoemission spectroscopy, we performed systematic electronic structure studies on well-known compound Cd3As2. For the first time, we observe a highly linear bulk Dirac cone located at the Brillouin zone center projected onto the (001) surface which is consistent with a 3D Dirac semimetal phase in Cd3As2. Remarkably, an unusually high Dirac Fermion velocity up to 10.2 \textrm{\AA}{\cdot}$eV (1.5 \times 10^{6} ms^-1) is seen in samples where the mobility far exceeds 40,000 cm^2/V.s suggesting that Cd3As2 can be a promising candidate as a hypercone analog of graphene in many device-applications which can also incorporate topological quantum phenomena in a large gap setting. Our experimental identification of this novel topological 3D Dirac semimetal phase, distinct from a 3D topological insulator phase discovered previously, paves the way for exploring higher dimensional relativistic physics in bulk transport and for realizing novel Fermionic matter such as a Fermi arc nodal metal., Comment: 4+ pages, 4 Figures, originally submitted in September (2013); Topological version was published at http://www.sciencemag.org/content/347/6219/294.full (Xu et.al., ScienceExpress 2014)

Using circular dichroism-angle resolved photoemission spectroscopy (CD-ARPES), we report a study of the effect of angular momentum transfer between polarized photons and topological surface states on the surface of highly bulk insulating topological insulator Bi2Te2Se. The photoelectron dichroism is found to be strongly modulated by the frequency of the helical photons including a dramatic sign-flip. Our results suggest that the observed dichroism and its sign-flip are consequences of strong coupling between the photon field and the spin-orbit nature of the Dirac modes on the surface. Our studies reveal the intrinsic dichroic behavior of topological surface states and point toward the potential utility of bulk insulating topological insulators in device applications., Comment: 5 pages, 4 figures

Quantitative understanding of the relationship between quantum tunneling and Fermi surface spin polarization is key to device design using topological insulator surface states. By using spin-resolved photoemission spectroscopy with p-polarized light in topological insulator Bi2Se3 thin films across the metal-to-insulator transition, we observe that for a given film thickness, the spin polarization is large for momenta far from the center of the surface Brillouin zone. In addition, the polarization decreases significantly with enhanced tunneling realized systematically in thin insulating films, whereas magnitude of the polarization saturates to the bulk limit faster at larger wavevectors in thicker metallic films. Our theoretical model calculations capture this delicate relationship between quantum tunneling and Fermi surface spin polarization. Our results suggest that the polarization current can be tuned to zero in thin insulating films forming the basis for a future spin-switch nano-device., Comment: 8 pages, 4 figures

The Kondo insulator SmB6 has long been known to exhibit low temperature (T < 10K) transport anomaly and has recently attracted attention as a new topological insulator candidate. By combining low-temperature and high energy-momentum resolution of the laser-based ARPES technique, for the first time, we probe the surface electronic structure of the anomalous conductivity regime. We observe that the bulk bands exhibit a Kondo gap of 14 meV and identify in-gap low-lying states within a 4 meV window of the Fermi level on the (001)-surface of this material. The low-lying states are found to form electron-like Fermi surface pockets that enclose the X and the Gamma points of the surface Brillouin zone. These states disappear as temperature is raised above 15K in correspondence with the complete disappearance of the 2D conductivity channels in SmB6. While the topological nature of the in-gap metallic states cannot be ascertained without spin (spin-texture) measurements our bulk and surface measurements carried out in the transport-anomaly-temperature regime (T < 10K) are consistent with the first-principle predicted Fermi surface behavior of a topological Kondo insulator phase in this material., Comment: 4 Figures, 6 Pages

The surface of topological insulators is proposed as a promising platform for spintronics and quantum information applications. In particular, when time- reversal symmetry is broken, topological surface states are expected to exhibit a wide range of exotic spin phenomena for potential implementation in electronics. Such devices need to be fabricated using nanoscale artificial thin films. It is of critical importance to study the spin behavior of artificial topological MBE thin films associated with magnetic dopants, and with regards to quantum size effects related to surface-to-surface tunneling as well as experimentally isolate time-reversal breaking from non-intrinsic surface electronic gaps. Here we present observation of the first (and thorough) study of magnetically induced spin reorientation phenomena on the surface of a topological insulator. Our results reveal dramatic rearrangements of the spin configuration upon magnetic doping contrasted with chemically similar nonmagnetic doping as well as with quantum tunneling phenomena in ultra-thin high quality MBE films. While we observe that the spin rearrangement induced by quantum tunneling occurs in a time-reversal invariant fashion, we present critical and systematic observation of an out-of-plane spin texture evolution correlated with magnetic interactions, which breaks time-reversal symmetry, demonstrating microscopic TRB at a Kramers' point on the surface., Comment: 12 pages, 3 Figures, Related results at http://online.kitp.ucsb.edu/online/topomat11/hasan/oh/01.html

We perform systematic angle-resolved photoemission spectroscopic measurements on the lead tin telluride Pb1-xSnxTe pseudobinary alloy system. We show that the (001) crystalline surface, which is a crystalline surface symmetric about the (110) mirror planes of the Pb1-xSnxTe crystal, pos- sesses four metallic surface states within its surface Brillouin zone. Our systematic Fermi surface and band topology measurements show that the observed Dirac-like surface states lie on the symmetric momentum-space cuts. We further show that upon going to higher electron binding energies, the surface states' isoenergetic countours in close vicinity of each X point are observed to hybridize with each other, leading to a Fermi surface fractionalization and the Lifshitz transition. In addition, systematic incident photon energy dependent measurements are performed, which enable us to un- ambiguously identify the surface states from the bulk bands. These systematic measurements of the surface and bulk electronic structure on Pb1-xSnxTe, supported by our first principles calculation results, for the first time, show that the Pb1-xSnxTe system belongs to the topological crystalline insulator phase due to the four band inversions at the L points in its Brillouin zone, which has been recently theoretically predicted., Comment: 4 pages, 4 Figures, Submitted May '12

Using angle-resolved photoemission spectroscopy, we report electronic structure for representative members of ternary topological insulators. We show that several members of this family, such as Bi2Se2Te, Bi2Te2Se, and GeBi2Te4, exhibit a singly degenerate Dirac-like surface state, while Bi2Se2S is a fully gapped insulator with no measurable surface state. One of these compounds, Bi2Se2Te, shows tunable surface state dispersion upon its electronic alloying with Sb (SbxBi2-xSe2Te series). Other members of the ternary family such as GeBi2Te4 and BiTe1.5S1.5 show an in-gap surface Dirac point, the former of which has been predicted to show nonzero weak topological invariants such as (1;111); thus belonging to a different topological class than BiTe1.5S1.5. The measured band structure presented here will be a valuable guide for interpreting transport, thermoelectric, and thermopower measurements on these compounds. The unique surface band topology observed in these compounds contributes towards identifying designer materials with desired flexibility needed for thermoelectric and spintronic device fabrication., Comment: 9 pages, 6 figures; Related results at http://online.kitp.ucsb.edu/online/topomat11/hasan/

It is predicted that electrons on the surface of a topological insulator can acquire a mass (massive Dirac fermion) by opening up a gap at the Dirac point when time-reversal symmetry is broken via the out-of-plane magnetization. We report photoemission studies on a series of topological insulator materials focusing on the spectral behavior in the vicinity of the Dirac node. Our results show that the spectral intensity is suppressed resulting in a "gap"-like feature in materials with or without any magnetic impurity or doping. The Zeeman gap in magnetically doped samples, expected to be rather small, is likely masked by the non-magnetic strong spectral weight suppression involving a large energy scale we report. The photoemission spectral weight suppression observed around the Dirac node thus cannot be taken as the sole evidence for a time-reversal symmetry breaking magnetic gap. We discuss a few possible extrinsic and kinematic origins of the Dirac point spectral weight suppression ("gap") observed in many commonly studied topological materials., Comment: 10 pages, 3 Figures

We perform spin-resolved and spin-integrated angle-resolved photoemission spectroscopy measurements on a series of compositions in the BiTl(S1-xSex)2 system, focusing on x-values in the vicinity of the critical point for the topological phase transition (the band inversion composition). We observe quasi two dimensional (2D) states on the outer boundary of the bulk electronic bands in the trivial side (non-inverted regime) of the transition. Systematic spin-sensitive measurements reveal that the observed 2D states are spin-momentum locked, whose spin texture resembles the helical spin texture on the surface of a topological insulator. These anomalous states are observed to be only prominent near the critical point, thus are possibly related to strong precursor states of topological phase transition near the relaxed surface., Comment: 5 pages, 4 figures

The striped cuprate La$_{2-x}$Ba$_x$CuO$_4$ ($x=\frac18)$ undergoes several transitions below the charge-ordering temperature $T_{co}$ = 54 K. From Nernst experiments, we find that, below $T_{co}$, there exists a large, anomalous Nernst signal $e_{N,even}(H,T)$ that is symmetric in field $H$, and remains finite as $H\to 0$. The time-reversal violating signal suggests that, below $T_{co}$, vortices of one sign are spontaneously created to relieve interlayer phase frustration., Comment: 5 pages, 4 figures